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Barren plateaus are a central bottleneck in the scalability of variationalquantum algorithms (VQAs), and are known to arise in various ways, from circuitdepth and hardware noise to global observables. However, a caveat of mostexisting results is the requirement of t-design circuit assumptions that aretypically not satisfied in practice. In this work, we loosen these assumptionsaltogether and derive tight upper and lower bounds on gradient concentration,for a large class of parameterized quantum circuits and arbitrary observables.By requiring only a couple of design choices that are constructive and easilyverified, our results can readily be leveraged to rule out barren plateaus forexplicit circuits and mixed observables, namely, observables containing anon-vanishing local term. This insight has direct implications for hybridQuantum Generative Adversarial Networks (qGANs), a generative model that can bereformulated as a VQA with an observable composed of local and global terms. Weprove that designing the discriminator appropriately leads to 1-local weightsthat stay constant in the number of qubits, regardless of discriminator depth.Combined with our first contribution, this implies that qGANs with shallowgenerators can be trained at scale without suffering from barren plateaus --making them a promising candidate for applications in generative quantummachine learning. We demonstrate this result by training a qGAN to learn a 2Dmixture of Gaussian distributions with up to 16 qubits, and provide numericalevidence that global contributions to the gradient, while initiallyexponentially small, may kick in substantially over the course of training.

From Tight Gradient Bounds for Parameterized Quantum Circuits to the Absence of Barren Plateaus in QGANs